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Relations and Functions

Short Answer Type

21.

Let A = {a, b, c}, B = {d, e, f}, C = {g, h, k}, L = {b, c}, M= {d, e} and N = {g, k}.

verify that $space space space space space space space space open parentheses straight L cross times straight M cross times straight N close parentheses subset of open parentheses straight A cross times straight B cross times straight C close parentheses$ .

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22. Let A = {a, b), B = {c, d}. Write A x B. How many subsets will A x B have? List them.

A x B = {a, b} x (c, d) = {(a, c), (a, d), (b, c), (b, d)}

Number if subsets if A x B = 2^{n(A x B)}= 2⁴= 16

The sunsets are : $space space straight ϕ$ , {(a, c)}, {(a, d)}, {(b, c)}, {(b, d)}, {(a, c), (a, d)}, {(a, c), (b, c)}, {(a, c), (b, d)}, {(a, d), (b, c), {(a, d), (b,, d), {(b, c) (b, d)}, {(a, c), (a, d), (b, c)}, {(a, c), (a, d), (b, d)}, {(a, c), (b, c), (b, d),{(a, d), (b, c), (b, d), {(a, c), (a, d), (b, c), (b, d)}

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23.

$space space space space space space space space space space space space space If space straight A bottom enclose subset of straight B comma space then space prove space that space straight A space straight x space straight A space equals space left parenthesis straight A space straight x space straight B right parenthesis intersection left parenthesis straight B space straight x space straight A right parenthesis$

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24.

Let A = {2, 3}, B = {1, 2, 3, 4}, verify that $space space space space space space space space space space space space straight A cross times straight A equals left parenthesis straight A cross times straight B right parenthesis intersection left parenthesis straight B cross times straight A right parenthesis$

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25.

If A and B are any two non-empty sets, then prove that

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